Question

In 2000, the population of Snowy Egrets went from 5,000 individuals to 15,000 individuals. What is the growth rate over those 4 years?

Answer 1

Answer:

$x=\sqrt[4]{3}-1$ or $x=0.316$

Step-by-step explanation:

To write this equation you would need to use this equation for growth.

Final amount=initial amount (1+growth rate)^time

We have the final amount, 15,000, the initial amount, 5,000, and the time, 4 years. Now we have to plug in the values. We can write the growth rate as x.

$15,000=5000(1+x)^4$

Now start by dividing both sides by 5000.

$\frac{15000}{5000} =(1+x)^4$

$3=(1+x)^4$

Now you can find the fourth root of both sides to get rid of the exponent.

$\sqrt[4]{3} =1+x$

Finally, subtract 1 from both sides.

$x=\sqrt[4]{3}-1$

And, if allowed, you can use a calculator to find the value in decimal form which would be:

$x=0.316$